Gravitational wave sources from inspiralling globular clusters in the Galactic Centre and similar environments

Abstract

We model the inspiral of globular clusters (GCs) towards a galactic nucleus harbouring a supermassive black hole (SMBH), a leading scenario for the formation of nuclear star clusters. We consider the case of GCs containing either an intermediate-mass black hole (IMBH) or a population of stellar-mass black holes (BHs), and study the formation of gravitational wave (GW) sources. We perform direct summation N-body simulations of the infall of GCs with different orbital eccentricities in the live background of a galaxy with either a shallow or steep density profile. We find that the GC acts as an efficient carrier for the IMBH, facilitating the formation of a bound pair. The hardening and evolution of the binary depends sensitively on the galaxy's density profile. If the host galaxy has a shallow profile, the hardening is too slow to allow for coalescence within a Hubble time, unless the initial cluster orbit is highly eccentric. If the galaxy hosts a nuclear star cluster, the hardening leads to coalescence by emission of GWs within 3-4 Gyr. In this case, we find an IMBH-SMBH merger rate of ΓIMBH-SMBH = 2.8 × 10-3 yr-1 Gpc3. If the GC hosts a population of stellar BHs, these are deposited close enough to the SMBH to form extreme mass ratio inspirals with a merger rate of ΓEMRI = 0.25 yr-1 Gpc3. Finally, the SMBH tidal field can boost the coalescence of stellar black hole binaries delivered from the infalling GCs. The merger rate for this merging channel is ΓBHB = 0.4-4 yr-1 Gpc3.